Question

log base5 20 * log base20 125. How do I find the exact value of this expression?

Answer 1

log_b(x) = log_a(x)/log_a(b)

Answer 2

rewrite log_20(125) in terms of log_5 using the above

Answer 3

use change of base

\[\log_{a}(b) = \frac{\ln(b)}{\ln(a)}\]

it doesn't matter if you use base 10 or base e logs

so your problems becomes

\[\frac{\ln(20}{\ln(5)} \times \frac{\ln(125)}{\ln(20)}\]

now you can use some log laws and find common factors

\[\frac{\ln(20)}{\ln(5)} \times \frac{\ln(5^3)}{\ln(20)}\]

good luck with completing the answer.